A possible start would be to search: privatization, in the site search or publications pages of organizations such as the International Monetary Fund. IMF gets 16 hits, including State-Owned Banks, Stability, Privatization, and Growth. But the World Bank gets 100,000+ hits for the site search: privatization; 19,000+ for: privatization banks statistics; and 201 even for: "privatizing banks" statistics. An easily compiled figure for worldwide public vs. privately owned banks seems to be very elusive, based on many searches I have tried. But I hope there are some RadRef librarians that have a bit more experience than I do - with both statistics and with public documents. Possibly, search.usa.gov might help, because it includes state as well as federal websites, reports, studies, etc. and gets "about 225 results" for the search: "financial sector" privatization worldwide statistics.
I know that the majority of the world's national banks, such as the Federal Reserve in the U.S. and the Bank of England are privately owned central banks that borrow money from international banking corporations. But a few countries, like Libya and China, have banks that are wholly owned by the state, which prints its own national currency. Other than these two, are there any other countries that follow this model? Where do I start looking to find out what percentage of ownership a state has in its national bank?